A spacetime whose metric is in the Kerr-Schild form (REF ) has a simple proposal for its
single copy. The vacuum Einstein equations further guarantee that the single copy field is on-shell.
The Kerr-NUT-(A)dS metric (REF ) can be written in a similar way: a multi-Kerr-Schild
form about a flat (or dS/AdS for nonzero \(\lambda \) ) background metric
\(\mathring{\mathbf {g}}\)  asThe background \(\mathbf {\mathring{g}}\)  matches
the Kerr-NUT-(A)dS metric when all \(M_{k}\)  vanish, although it does not take the same form in canonical coordinates.
There is a coordinate system in which it does have the same metric components as the corresponding Kerr-NUT-(A)dS
metric; see [1]} for details. Such “Kerr-Schild” coordinates are convenient when computing the
flat limit of derivatives.
\( \mathbf {g} = \mathring{\mathbf {g}} + 2 \sum _{k = 1}^{n} \frac{M_{k}x_{k}^{1-\varepsilon }}{U_{k}}\mu ^{k} \mu ^{k},\) 
